what is the doamin of f(x) = x3 − 6x + 7 (using interval notation)

Answer 1

The domain, the possible values of x, are all real numbers. In interval notation that's (-infinity, infinity)

x can take on any value between negative infinity and positive infinity. You have parentheses rather than brackets to indicate x does not ever equal infinity or negative infinity, as they are not numbers.

take the derivative of f(x). f'(x)=3x²-6 set it equal to zero and solve for x

3x²-6 = 0

3x² = 6

x² = 6/3 = 2

x = plus or minus square root of 2 or approximately -1.414 and +1.414

That gives the local maximum and local minimum for f(x) if you plug that into the original cubic equation. f(1.414)=1.34 f(-1.414) = -4.31 These are only limits for a local area, they are not global limits on the value of f(x)

There are no limits to f(x) either. It takes on all real numbers, from (-infinity,+infinity) You usually write infinity as an 8 on its side.

Domain and range include all real numbers. The graph starts very negative goes up reaches a local maximum turns downward then reaches a local minimum, then goes upward without limit.